- #1
ehrenfest
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Homework Statement
A point P is located in the interior of an equilateral triangle ABC. Perpendiculars drawn from P meet each of the sides in points D,E,F, respectively. Where should P be located to make PD + PE + PF a maximum? What about a minimum?
Homework Equations
The Attempt at a Solution
From symmetry considerations. I think that the maximum will be at the incenter. I am not sure about the minimum. Maybe at a vertex, but that is not really in the interior... I tried the standard reflections. I am not sure if I actually need to set up a coordinate system with P at the origin... That looks like it could get messy? I am also not sure how to use the fact that this is an equilateral triangle.